This invention relates to the decoding of phase shift keying (PSK) modulated signals suitable for a communication system and, more particularly, to a system for mapping inphase (I) and quadrature (Q) components in a vectorial representation of phase angle into four branch metrics and one sector number, suitable for use as a preprocessor unit before the core of a Viterbi decoder as in 8-PSK and 16-PSK pragmatic TCM decoders.
PSK modulated signals are often used in systems for communicating data. In such a signal, a carrier is modulated with stepwise increments of phase, such as 90xc2x0 steps in a quadrature PSK modulation, 45xc2x0 steps in an 8-PSK modulation, and steps of 22.5xc2x0 in a 16-PSK modulation. Typically, such a communication system would include, at its transmission end, a source of carrier signal, and a PSK modulator responsive to an input binary data signal for modulating the carrier signal. At its receiving end, the communication system would include some form of a phase demodulator, or decoder, suitable for extracting from the carrier instantaneous values of its phase shift and the data represented by the phase shift modulation. A suitable decoder is a Viterbi decoder which is operative to demodulate the phase modulation, the accuracy of the demodulation being dependent on the amount of electrical noise which may be received along with the modulated signal.
The near optimum operation of a Viterbi decoder in the detection of PSK signals can be accomplished by use of a preprocessor which identifies each of the possible phase states in the received PSK signal. Presently available preprocessors suffer from the disadvantage of an excessive amount of circuitry, particularly memory.
The foregoing disadvantage is overcome and other benefits are provided by a phase calculation system which, in accordance with the invention, enables a reduction in the amount of the circuitry in the pre-processor, while providing a digital representation of phase states suitable for operation of a Viterbi decoder.
In the case of a PSK modulation which provides numerous increments of phase shift, such as a 16-PSK modulation having 16 separate phase states, the modulation encompasses 360xc2x0 of phase shift. In the 16-PSK modulation, all of the phase states are spaced apart by equal phase increments of 22.5xc2x0, and may be represented by a set of vectors extending radially outward from a common origin. At the receiving end of the communication system, it is common practice to detect the values of phase shift by implementation of both inphase and quadrature channels. The signals outputted by the two channels constitute, respectively, I and Q components of the vector representing a present value of the carrier phase and magnitude.
It is possible to provide a memory storing a tabulation of all possible values of I and Q with the corresponding phase angle of the vector. Such a tabulation would involve more circuitry and consume more power than would be necessary to accomplish the task of determining the value of carrier phase.
PSK modulation is defined as a constellation of points on a circle separated by equal angles. In accordance with the invention, the sectors are defined as the regions between two vectors emanating from the origin of a circle and passing through the adjacent constellation points. The sectors are divided into equal number of smaller regions which, for convenience, may be referred to as sub-sectors. The sub-sectors divided into two smaller regions each of which, for sake of convenience, may be referred to as PIE (by analogy with sectors of a circular cake or pie). Further, in accordance with the invention, there has been found a set of four binary-formulated numbers, referred to as branch metrics, which represent the reliability that the corresponding constellation point was transmitted. The branch metrics are suitable for introduction into Viterbi decoder for enhanced operation of the Viterbi decoder. The mapping of constellation points to branch metrics is not unique over the complete constellation. In fact, the set of branch metric values in one sector, appear in some permuted version in all other sectors.
There are an even number of sectors in a quadrant, two sectors being present in 8-PSK and four sectors being present in 16-PSK. In each sector there are provided nine sub-sectors of which each of the first and ninth sub-sectors consist of only half as many PIEs as each of the remaining sub-sectors (the second through the eighth). By way of example, in the 16-PSK there are two PIEs for each of the second through the eight sub-sectors while the first and the ninth sub-sectors at the end of the sector have only one PIE each. For the 8-PSK, there are twice as many PIEs for each sub-sector as in the 16-PSK.
In the forgoing arrangement of the sub-sectors in each of the sectors, there is established a one-to-one correspondence between each sub-sector and a particular four-value branch metrics. By permutation of the four values of the branch metric terms, there are provided identifications for the sub-sectors if each of any other sectors, and other quadrant.
The foregoing identification of the sub-sectors within a quadrant provides for sufficient resolution of the sectors in the measurement of phase angle to insure an accurate measurement of the phase angle in PSK modulation. The same set of branch metrics appearing in any one quadrant appears in each of the other quadrants. Therefore, identification of any one of the 16 values of phase shift (for 16-PSK modulation) or any one of the 8 values of phase shift (for 8-PSK modulation) is accomplished by use of two identifiers. The first identifier is the quadrant established by the signs, positive or negative, of the I and the Q components. The second identifier is the corresponding sector number of the first quadrant. These two identifiers are employed readily to determine the branch metrics which are used by a decoder to determine the value of a phase angle, even in the presence of noise.